Model based design is a standard practice within the aerospace industry. However, the accuracies of these models are only as good as the parameters used to define them and as a result a great deal of effort is spent on model tuning and parameter identification. This process can be very challenging and with the growing complexity and size of these models, manual tuning is often ineffective. Many methods for automated parameter tuning exist. However, for aircraft systems this often leads to large parameter search problems since frequency based identification and direct gradient search schemes are generally not suitable. Furthermore, the cost of experimentation often limits one to sparse data sets which adds an additional layer of difficulty. As a result, these search problems can be highly sensitive to the definition of the model fitness function, the choice of algorithm, and the criteria for convergence. In this paper, the challenge of setting up an effective parameter identification scheme is explored in the context of an aircraft Power Thermal Management System (PTMS) model. Through simulation case studies, the performance of a gradient approximation and an evolutionary search method are evaluated using four different fitness functions and a variety of solver options. The gradient approximation method was observed to be best suited for problems in which knowledge of the system could be used to improve the fitness function and to help remove local minima. It performed the best with a min-max normalized fitness function which weighs error terms according to measurement type. The evolutionary search was observed to be more robust to local minima and less sensitive to the choice of fitness function. In both cases, the choice of solver options had a significant impact and a model to model test of the parameter identification method is recommended for tuning these settings.